Question

1. Your uncle is planning for retirement, and he wants to buy an annuity that will provide him with $96,000 of income a year for 20 years, with the first payment coming immediately. The market rate on this annuity is 5.25%. How much would the cost be today?

Answer just the dollar amount without the + or - sign. Round to the nearest dollar.

2. What's the value today of $1,950 to be received in 5 years if the appropriate interest rate is 6%, compounded monthly?

Answer just the dollar amount without the + or - sign. Round to the nearest dollar.

3. A 10-year bond has an 8% coupon, and an 8-year bond has a 10% coupon. Neither is callable, and both have the same yield to maturity. If the yield to maturity of both bonds increases by the same amount, which of the following statements would be CORRECT?

Group of answer choices

The prices of the two bonds would remain constant.

The prices of both bonds would decrease by the same amount.

The prices of both bonds would increase by the same amount.

One bond's price would increase, while the other bond’s price would decrease.

Both bonds would decline in price, but the 10-year bond would have the greater percentage decline in price.

4. Suppose a public company offers a bond for $587.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed by the company for $1,000. What interest rate would you earn if you bought this bond at the offer price?

Answer just the number without the % sign. Round to two decimal places.

5.

You open an investment account that pays 6% interest and deposit $1,250 today, compounded annually. How much will your account's ending balance be at the end of 25 years?

Answer just the dollar amount without the + or - sign. Round to the nearest dollar.

Answer 1

1. Since the question is asking that first payment will arise Immediately therefor it is the annuity due.

Formula for calculation of Present value of equal cash flow arising for definite period = Amount of inflow *[1+Present value annuity factor of R%, n-1 years)]

ie = $96000*[1+ Present value annuity factor(0.0525, 19 years)

= $96000*12.8428

= $1232909

2. Given is the amount to be received after 5 years from with monthly compounding is $1950.

Formula for compound interest calculation is A= P(1+r/n)^nt

^{where A = Amount received after 5 years as per question ie $1950}

^{P = Principle amount invested let say x in this question}

^{R = Rate of interest ie 6% pa}

^{n = No. of times interest is compounded ie monthly of 12 times}

^{nt = total no. of time interest is calculated ie 5*12 = 60 in this question}

Putting the values in the formula >>> $1950 = x(1+0.06/12)⁶⁰

^{>>> $ 1950 = x(1.3488)}

^{>>> x= $1446}

^{3. As we know YTm and Bond value is having inverse relationship ie if YTM increases bond value will decrease and vice versa.}

^{Therefore both bond will be having decline in price with YTM increase however the bond having higher tenure will be having more decline in price.}

4. Given is the present value of the bond = $587.25

Maturity value after 5 years = $1000

Rate of interest = ?

As we know Present Value = Future Value/(1+r)ⁿ

Where n = 5 years

Now putting the values in formula and calculating the same >>> $587.25 = 1000/(1+r)⁵

^{>>> r = 11.25% Approx...}